CBS has full episodes of "classic" television shows for you to watch, including the original Star Trek (three seasons), Hawaii Five-0 (one season), MacGyver (one season), the Twilight Zone (two seasons), and Melrose Place (one season). Melrose Place? How did that get in there?
"Where no man has gone before" still creeps me out especially the glowing eyes. It was supposed to be the first episode but the network execs thought it was too much? So it ended up the third episode. Something like that. But it was the "NO KILL I" episode that had me hiding behind the neighbor's living room chair in 1967.
If you don't consider those "classic", TVLand has some full episodes of the Andy Griffith Show, the Beverley Hillbillies, and Gunsmoke.
NBC has Miami Vice (but I can't find the infamous "Glades" episode), the A Team, and Alfred Hitchcock for your vintage viewing pleasure.
ABC is a little light on the classics, unless you consider My So-Called Life classic :)
AOL has full episodes of Lost in Space (ugh), Alias Smith and Jones, the Bob Newhart Show (now there's a classic), and clips from Iconoclasts, which isn't old enough to be classic, but I though the episode of Sean Penn and Jon Krakauer in Alaska talking about making the Into the Wild movie was good.